What do you see?
- A girl is pushing a guy around on a chair. She is making it seem like he is actually on a roller coaster. She is changing directions really fast
What do you think?
- Going down because I believe the stomach drops and you feel really strange and you are going so fast.
Kingda Kaaaaa
- Kingda Ka is a thrilling ride that s located at Six Flags Great Adventure. It is very popular because of its major drop. The ride is a fast ride that only takes like 20 seconds, but the wait is the most thrilling part. You start off by going up really high until you reach the top and come down at a very fast speed. Due to the coaster going so fast, the coster needs to turn on the way down because of the speed. http://www.sixflags.com/greatadventure/rides/kingdaka.aspx
Nitro
- Nitro also a thrilling ride and is also located at SIx Flags Great Adventure. It is a typical roller coaster made of steel and it moves very fast. Many riders love the thrill of the flips and fast turns that this ride provides. This is also not a slow ride, at it's top speed Nitro can go about 80 mph. http://www.ultimaterollercoaster.com/coasters/yellowpages/coasters/nitro_sfgadv.shtml
Physics Talk
scalar: a quantity that has magnitude, but no direction (opposite of a vector) speed: distance traveled divided by time elapsed. scalar vector: a quantity that has both magnitude and direction displacement: the difference in positions; it depends only on the endpoints, not on the path. vector velocity: displacement divided by the time elapsed(vector) acceleration: the change in velocity divided by the time elapsed. (vector)
Checking up q 1-4 1. The distance is scalar (no direction) and displacement is vector (direction). I 2. Going to school and back, the displacement is 0 3. speed is distance/time- scalar and velocity is displacement/time- vector 4. acceleration = change in velocity / time elapsed
Physics to Go 1.
2. The cause of the thrills is during the accelerations along the curve, drops, and horizontal circles.
3. a) The smaller the radius higher speed. There is more distance to travel and there is less thrills because you are traveling at constant speed
b) V = 40000/ t t = 24 hours
V = 1,666.7 km/hour
4. a = v/t
= 12/4m/s2
= 3 m/s2
5. a) speed
b) velocity
c) velocity
d) displacement velocity
e) displacement
6. v = d/t v = .1m/2s .05 m/s 7. v = d/t .05 m/s = .05m / s s = 1 8. a = change in V / change in t a = 25 m/s / 10s a = 2/5 (m/s)/2 10a) for young children I would make the back curve have a bigger radius so it is slower. For adults make the radius smaller so you go through faster. 10b)
What do you think Now?
Going down the first drop because that is when you have reached the fastest acceleration and you are not used to the speed. The flip is also thrilling but you are going so fast that it is hard to feel heavy.
Section 2
Physics Talk Gravitational Potential Energy and Kinetic Energy Energy Transformations in the Roller coaster GPE: the energy a body possesses as a result of its position in a gravitational field KE: the energy an object possesses because of its speed KE depends on speed, GPE depends on height, and both depend on mass GPE(J) KE(J)
mechanical energy: the sum of kinetic energy and potential energy
the sum of KE and GPE is the same at any point in the rollercoaster
when GPE increases, KE decreases and vice versa
Calculating KE from GPE
Calculating Speed from Kinetic and GPE
Mechanical energy (bottom) = mechanical energy (top)
KE (bottom) + GPE (bottom) = KE (top) + GPE (top)
1/2mv^2 (bottom) = mgh (top)
What goes up must come down?
What do you see?
- There is a roller coaster and the people in the first car is bored because they are going straight and slow. The second car the people are excited because they are going down a drop and they are going faster.
What do you think?
- The cart at the steeper angle because it is at a bigger angle and it will travel down the slope faster.
Checking up q 1-5
Physics to Go
1. They are the same because they start at the same height
3.
GPE
KE
GPE +KE
60,000
0
60,000
0
60,000
60,000
30,000
30,000
60,000
15,000
45,000
60,000
4.
5.
Mass of car = 300 kg and g = 10 N/kg or 10 m/s^2 (approximate value)
Position of car --> height (m)
GPE (J) = mgh
KE (J) = 1/2 mv^2
GPE + KE (J)
top (25 m)
=(300)9.8(25) 73,500 J
0 J
= 75,000 J
bottom (0m)
= (300)9.8(0)
0 J
75,000 J
=
75,000 J
halfway down (12.5 m)
=(300)9.8(12.5)
36,750 J
37,500 J
=
75,000 J
further down (5m)
= (300)9.8(5)
14,700 J
60,000 J
=
75,000 J
6.
7. GPE = mgh
= (.2)(9.8)(.75)
= 1.47 J
GPE = KE
mgh = 1/2mv^2
(9.8)(.75)
1/2v^23.83 m/s = v
GPE = KE mgh = 1/2mv^2 (9.8)h = 1/2(3.83)^2 h = .75 m
8. The speed will not change if there are 6 passengers or 26 passengers. The speed is independent of the mass of the car. This is because in the equation GPE (top) = KE (bottom), mass cancels out
9) a. The roller-coaster is traveling at its fastest at point B because its initial height was the highest before the drop. The smallest is GPE and the biggest is KE.
9) b. The roller-coaster is traveling at the same speed at points C and F. This is because their heights are the same. GPE and KE are equal to each other.
9) c. The roller-coaster is traveling faster at D because it was just dropped at point C. Other than traveling up at D. 10) b. The roller coaster cannot reach point H. This is because the height of the original GPE is less than the height of H. With GPE and KE equaling the each other, the height of H would make that it very hard to be higher. 11.
Position
Height (m)
GPE = mgh (J)
KE = 1/2mv^2 (J)
GPE + KE (J)
bottom of hill
= 0
= 0
= 50,000
= 50,000
top of hill
= 25
= 50,000
= 0
= 50,000
top of loop
= 15
= 30,000
= 20,000
= 50,000
horizontal loop
= 0
= 0
= 50,000
= 50,000
What do you think now?
- The one with the steeper drop because it feels like you are going down at a different angle. They both have the same speed, but the second one provides more acceleration than the first one. It is more thrilling due to the faster acceleration.
Section 3
What do you see? One of the kids launches the frog spring toy into the air. A lab partner is standing up with a ruler trying to eye down how high the toy goes into the air. There is also a photo gate towards the bottom of the launch immediately after the frog launches to get its velocity.
What do you think? To get to its highest point, the roller coaster slowly and gradually climbs up a big hill. No, it does not cost more to lift the people on the roller coaster. No matter how many passengers, the cart is going to make it to the highest point on the roller coaster track.
Physics Talk
Conservation of Energy
- Energy in a system can vary between KE GPE and EPE
- Spring Potential Energy: the energy stored in a spring due to its compression or stretch
ex of EPE: bungee cords, trampolines
EPE = SPE
- a bouncy ball does not get to the same height in each successive bounce because some of the energy is converted to sound/heat energy
- The total energy of an object can be GPE, SPE, or KE, but the sum of the energies is always to same
all energies are measured in joules, and total # of joules must always be the same
pop-up toy: GPE (bottom) KE & some GPE (just after leaving table) equal KE & GPE (halfway up) GPE (top)
a higher mass pop-up toy won't go as high as a lower-mass one even though both had the same SPE.
- The less massive and more massive pop-up toys can have the same GPE if the more massive pop-up toys don't go as high
- Since GPE = mgh, the larger mass has a smaller height and the smaller mass has a larger height
a roller coaster has all its GPE at the highest hill. This becomes KE as the coaster is released.
electric energy pulls the coaster up a hill. The electrical energy comes from a powerplant
after the cars are pulled up to the top of the hill, the total GPE and KE remains the same except for the losses due to thermal and sound energy
- As the breaks stop, KE is converted to thermal energy
- If brakes fail, a large spring may stop the car as the car compresses it
SPE = 1/2kx^2
k=spring constant
x=amount of stretch or compression of the spring
Checking Up Questions
1. As it bounces off of the table, all of the SPE transfers into gravitational potential energy and kinetic energy.
2. Because it has 2J of potential energy, the kinetic energy will be 2J as well.
3. When reaching maximum height, the GPE will be 2J.
4. EPE=1/2kx^2. K is the spring constant and x is the distance compressed/stretched.
Physics To Go
5. The second hill can't be higher than the first. It won't have enough gravitational potential energy to reach the top of the second hill.
6. The roller coaster doesn't travel forever. As it continues to move, it loses its kinetic energy and gravitational potential which turns into heat and sound energy. Then it can't travel forever. 2016730094
7. GPE= electric energy
(300)(9.8)(15)= electric energy
=44,100J
8a. KE= 1/2 mv^2
KE=1/2(400)(15)^2
=45,000J
8b. GPE=KE
=45,000 J
8c. 45,000= (400)(9.8)(h)
11.48 meters=height
9. As a ball is thrown upwards, because the height is increasing, the GPE increases because they are related.
10. The gain is the same for each path because they are all going up to the same height so they will all have the same gravitational potential energy at the end.
11a. They should have similar results because they are the same.
- The roller coaster needs to have enough speed to get up to the top of the hill. It also needs a strong enough wire to pull it up just in case it does not have enough speed. Also a chain and motor need to be present.
- Yes because the heavier the object the slower it travels up the hill, but the faster it travels down the hill. The more weight the more work. The more work, the more expensive it is to carry the people up.
Section 4
What do you see?
- The first picture they are very bored on the moon. The second picture they are more excited. It is because the moon has no gravity and mars has more gravity than the earth. The more gravity the faster they go.
What do you think?
- Yes. The gravity on earth pulls us towards the center of earth. That is why we can stand.
- Australia looks upside down to us because it is on the other side of the planet. They can stand in australia because on the earth the gravity is pulling towards the center of the earth.
Physics Talk
Newton's Law of Universal Gravitation
Gravitational field: the gravitational influence in the space around a massive object Earth of the source of its gravitational field because it is the first object that sets up in the space around it second object interacts with this field--moon (response/test object)
Inverse-Square Relationship acceleration due to gravity becomes less as an object moves further from the surface of Earth
Inverse-Square Relationship: the relationship between the magnitude of a gravitational force and the distance from the mass. this also describes how electrostatic forces depend on the distance from an electrical charge force of gravity between 2 objects decreases by the square of the distance between them Ex: if you triple (3x) the distance, the force is (1/9) the original
Newton's law of universal gravitation: all bodies with mass attract all other bodies with mass; the force is proportional to the product of the two masses and gets stronger as either mass gets larger; the force decreases as the square of the distances between the two bogies increases : the force of attraction between two bodies due to their masses Equation of Newton's law of universal gravitation Fg = (Gm1m2)/r^2 (Fg = force between the bodies, r = the distance between their centers, m1 & m2 = masses of the bodies, G = universal constant equal to 6.67 x 10^-11 The moon orbits Earth and the planets orbit the Sun in elliptical paths plants don't move in exact ellipses b/c planets tug on on another
Checking Up 1. The direction of the gravitational field in the classroom is to the ground 2. The gravitational field is the strongest near the surface of Earth 3. If you triple the distance between two masses, the force is (1/9) the original 4. Gravity is the force that holds the Moon in its orbit around Earth 5. The shape of the orbit of the plants around the sun is approximately elliptical.
Physics To Go
1. Originally, the gravitational force between two asteroids is 500 N. If the distance between them is doubled, the force would be 125 N (1/4 the original).
2a. Fg would be 1/4 of the original
2b. Fg is 1/9 original
2c. Fg is 1/16 original
3. Gravity is always trusted because it does its job of keeping all humans standing on their feet on the Earth. Gravity is always there because we never see floating objects.
4. Acceleration due to gravity (g) is highest at the bottom of a roller coaster, not the top.
5a. Water on the Earth's side facing the moon is closer to the moon than the center of Earth.
5b. Water moves independently to Earth. There are high tides on those bodies of water facing the moon. The gravitational field of the moon is attracted to the water, making the water rise to the forces. Water does not have as much mass as an entire planet (Earth).
5c. There is not an even distribution of water on the Earth's surface because there are bits of land scattered (islands) throughout the waters. All bodies of water are different distances from the moon and therefore, have different (stronger, weaker) impacted forces of the gravitational field of the moon. This is the inverse-square relationship. The further away from the moon, the more subtle the waves.
6a. If a fish was not impacted by gravity, it would be moved away from the water and into the air, becoming a floating object, and eventually, it will die.
6b. Gravity holds the fish in the water because the mass of a fish is much less than the mass of the Earth. Because masses attract, the large mass of Earth attracts to the small mass of the fish.
7a. 1/4
7b. 1/9
7c. 1/16
7d. 4x
8a. 2x
8b. 3x
8c. 4x
8d. 1/2x
9a. 4x
9b. 9x
9c. 16x
9d. 1/16x
10a. 2x
10b. 9x
10c. 6x
Physics Plus
1. a = v^2 / r 2. v = d/t (2 x pi x [3.84x10^8) / 2440800 v = 998.505 m/s 3. a = v^2 / r a = 998.505^2 / 3.84x10^8 a= 0.0025 m/s^2 4. It was pretty close to each other.
What do you think Now?
Gravity has a downward direction, or facing the center core of the Earth. Its the direction of the force on the mass. The earth is acting on the human. People in Australia are still held down to the ground even though gravity to us is supposed to have them upside down. Gravity attracts the mass of the people on earth to the center of the Earth, which means that the people are forced to the surface of the Earth.
Section 5
What do you see?
- Someone buying some type of meat. Weighing the meat by pushing down. In the second picture they are measuring in the air using a spring scale
- Different ways to measure things
What do you think?
- No because a canary will move around and you can't an exact measurement. The elephant is much heavier and might break a spring scale.
Physics Talk
Hooke's Law Describes the Restoring Force a Spring Exerts
Stretching a rubber band or a spring requires a force
There is a linear relationship between the amount of force required for each stretch of the spring.
It is a straight line.
Robert Hooke discovered this property of springs
stretch of spring is directly proportional to the force applied to it
If the spring is not moving, the spring exerts a restoring force equal in magnitude to the force that stretched the string.
Hooke's law: the restoring force exerted by a spring is directly proportional to the distance of stretch or compression of the spring
force exerted by the spring = -spring constant x spring stretch (or compression)
Fs = -kx
negative shows that the pull by the spring is opposite to the direction it is stretched or compressed
k is an indication of how easy or difficult it is to stretch/compress a spring
a stiff spring will have a large value for k; a soft spring will have a small value for k
Hooke's law : F = kx
Straight line: y = slope x
weight = mg
force = ma
weight: the force exerted on a mass as a result of gravity; the weight force on an object due to Earth is downward, in the vertical direction
Stretch and Compress
bathroom scales work by compressing a spring. When you step on the scape, the spring compresses just enough to provide an upward force equal to your weight. The more weight, the more compression of the spring is required. The spring is connected to a scale that has been calibrated to give your weight. As the spring compresses, the arrow points to a different number corresponding to the compression and force of the spring.
Checking Up Questions
1. If the force of the spring is increased 5 times, the stretch of the spring increases 5 times as well (direct relation)
2. Spring constant (k) displays the strength of a spring. The greater value of k, the stiffer the spring. The smaller, the weaker.
3. Mass (in kg) is a part of the weight equation. N=kg*m/s^2. Acceleration must equal 0.
4. The more weight that steps onto the scale, the more compression of the spring inside the scale.
Physics To Go
1a. w=mg
=(100kg)(9.8m/s^2)
=980 N
1b. w=mg
=(10kg)(9.8m/s^2)
=98 N
1c. w=mg
=(60)(9.8)
=588 N
2a. .25/130=1/x
x=578.5 N
2b. 4.45(1000)
x= 4,450 N
2c. 4.45(50)
x=222.5 N
3a.
3b. see above trend lines
3c. The slope of the graph is 14.913 N/m, which is the k (spring constant) value.
3d. The slope represents the k value. This shows the strength/stiffness or weakness of the spring.
3e. I purposefully made the second spring more weak. The slope is 1.8667 N/m. This is the k value, and it is weaker because it has a less steep slope. The spring is weaker than the other one.
4. Fs=-kx
12=k(.03)
k=400N/m
5. As the force of the spring increases, the stretch distance also increases. It is a direct relationship. When clearing the side that K is on, the equation becomes k=Force of spring divided by stretch distance. The greater the value of k, the greater the stiffness of the spring. Therefore, the more force, the less distance it stretches. When weight is added, the stretch distance will increases, but it may not be a dramatic increase. Negative sign indicates that the force is going in the opposite direction of the stretch distance.
6. The greater value of k, the more stiff the spring is. Therefore, 15.0 N/cm is more difficult to stretch.
7. slope= 150N/m *points of slope (.03,4.5)(.01,1.5)
8. A spring scale displays weight in newtons. When attaching masses, the scale stretches, and you can read the scale to determine the weight. It incorporates the mass added and the stretch distance that is created from adding mass. Therefore, it follows the y=-kx formula.
What do you think now?
The same scale can not weigh both a canary and an elephant. The scale works by the compression of a spring. The spring can only hold so much. The scale would be only able to read the maximum number of weight on it, and that will not be the full weight of the elephant. There is not enough distance for the spring to compress for the elephant to go onto the scale.
Section 6
What do you see?
- A big guy is standing on a scale and it is going down because he is so big. Then there is a small person who is getting pulled up because he is litter.
What do you think?
- Your weight does not change but it feels like it is. You are going up and down very quickly, and it throws your weight around.
- Yes because it is pulling you up which makes you seem like you are little and then when you are going down you are pushing down harder than normal.
Physics Talk
Newton's first law
- An object at rest stays at rest, or in motion stays in motion unless acted on by an unbalanced force.
Newton's second law
- unbalanced force creates an acceleration
- The bigger force is in the same direction
- To do this, draw Mation Map (draw FBD)
Checking Up 1. The sum of all the forces acting on an object when it is moving up at constant speed is zero. 2. When accelerating up on a bathroom scale on a roller coaster, the reading on the scale will be greater than your weight in magnitude. 3. You feel as if your weight is more when you accelerate upward because of contact forces and stretching stomach tissues, and forces are holding your stomach in place 4. If the elevator cable were to break, you would only have the force of your weight pulling you down & nothing pushing you up. The force reading on the scale would be zero and you'd feel weightless. 5. Air resistance slows a falling raindrop.
Physics to Go 1. a. (9.8)(2) = 19.6 m/s b. (9.8)(5) = 49 m/s c. (9.8)(10) = 98 m/s 2 a. (1.6)(2) = 3.2 m/s b. (1.6)(5) = 8 m/s c. (1.6)(10) = 16 m/s
4.
Motion of the Elevator
Acceleration (up, down, zero)
Relative Scale Reading (greater, less or equal to weight)
At rest, bottom floor
zero
equal
Starting at Rest, Increasing Up
up
greater
Continuing to move, Constant Up
zero
equal
Slowing down to top floor, Decreasing Up
down
less
At rest, top floor
zero
equal
Starting at rest, Increasing Down
down
less
Continuing to move, Constant Down
zero
equal
Coming to a stop on the ground floor
up
greater
5. A student who 150 lb and is 148 lb on a scale on an elevator has increased down acceleration, or they decreased their acceleration upward. 6. The person will observe that his weight increases. An increased upward acceleration increases the weight on the scale because the force that the scale is exerting is greater than the force of weight exerted downward.
7
a. When the elevator starts to descend the scale's reading will decrease.
b. Fnet = ma
F=ma
N-mg = ma
N= ma +mg
= (50-1.5) +(50x9.8)
= 415 N
8
a. Scale = 0
w= mg= 50x9.8
= 490 N
b. velocity up/ acceleration up/ f is up
N-mg = ma
N= 50(2) + 490
N= 590 N
c. N-w = ma
N
w= 4909
a. At rest, the force up (scale) and force down (gravitation) are both equal, so the Fnet is zero. When the Fnet = zero, the scale reads your accurate weight.
b. An elevator in free fall has no force from a scale pushing up, so there is only the force of you pushing down. Therefore, the scale reads as 0.
c. The scale reads a greater number than at rest because it is accelerating upward. When acceleration up, that means the bigger force is in the Fscale. When Fscale is bigger than the weight, the number is positive, and the scale will read a higher number.
10. They would find the loops exciting because they feel heavier the whole time in the loop. They'd also like the change between increasing upward/downward acceleration and decreasing upward/downward acceleration. The increase acceleration upward would make them feel heavy and the increase down would change their feeling to light. The decrease upward would then keep them feeling light, but the decrease downward would have them feeling heavier.
Notes Increasing SPeed: Velocity and Acceleration point in the same direction -->(v) -->(v) --> (v) -->(a) Decreasing Speed: Velocity and acceleration point in opposite directions -->(v) -->(v) --> (v)
<--(a)
F and acceleration ALWAYS POINT in same DIRECTION
The Bigger force is in same direction as F
What do you think Now?
- No. Your weight does not change because your weight is always the same. Lets say I am standing on a bathroom scale, my weight will not change unless I go up and down because it is a change of direction. If you are going up your acceleration is up and you will be heavier than normal. If you are going down your acceleration will be down and the measurement of your weight on the scale will be smaller.
Section 7
What do you see?
- I see a roller coaster with a bunch of turns and loops. It seems like it is very scary and life threatening because the person in the cart is falling off the tack.
What do you think?
- It is because the carts have so much momentum that they can carry through the entire loop.
Physics Talk
Centripetal Force
- force that points to the center of the circle
- It can either be Normal, Tension, Weight,
Centripital acceleration
- Always points to the center of the circle
- The Speed is constant
- If the centripetal acceleration is equal to 0 then you are moving in a straight line
- Fc= mv^2/r
- The force, net force, and acceleration all point to the center of the circle
safety
- Less than 3 g's is safe for regular people
- Trainer people like astronauts can do like 6 g's
Checking up
1. Centripital force
2. Yes. You must or else you will fall
3. Weight and Normal
4. Normal
5. Mass it is direct relationship and on the radius it is inverse and speed is direct squared
Physics to go 1a. The path is a circle
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1b. If the string breaks, the car would travel on a tangent to the circular path.
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2a. Friction of the tires replaces the string of the car. 2b. If hitting a patch of ice, you will go tangent to the circular path.
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6a. The speed did not change. Velocity has changed. 6b. The velocity changed because it changed direction. 6c. delta V=Vf-Vi 20^2 + 20^2 = c^2 c = 28.2 m/s tan-1 = 20/20 theta = 45 degrees 7. Ac=v^2/r =20^2/200 = 2 m/s^2 13a. Bottom of hill #1- heavier 13b. Top of vertical loop- uncertain 13c. Bottom of vertical loop- heavier 13d. Bottom of hill #2- heavier 13e. Lift hill (going up at constant speed)- "normal"
14a. Bottom of hill #1- up 14b. Top of vertical loop- down 14c. Bottom of vertical loop- up 14d. Bottom of hill #2- up 14e. Lift hill (going up at constant speed)- zero 14f. Horizontal loop- to center 14g. Back curve- to center
Physics Plus 1. a. As mass increases, the net force increases. They share a direct relationship.
b. The velocity and the net force share a direct-square relationship. 2. Fc=mv^2/r. If velocity is doubled, the force needs to be 4 times as strong because of the direct square relationship. 3.The Fnet decreases because the radius increases. 4. The larger radius for the curve, the LESS the force required to keep the car moving along a curve. If the curve is tight, than a GREATER force is required. 5.The more string that was let out, the less force was needed. 6. a. Ac=v^2/r =12^2/20 =7.2 m/s^2 b. Fc=mv^2/r = (300)(12^2)/20 =2160 N
What do you think Now? - You feel pressed into your seat due to inertia. The net force has to point to the center because if it doesn't then you will fall to the ground. You will not fall because of the forces acting on you that cause you to stick to the cart.
Section 8
Physics Talk work: the product of displacement and the force in the direction of the displacement; the energy transferred to an object W = force (parallel to the displacement) x displacement -W is the same regardless to the angle of the incline -Force is larger on a steeper incline ; but the distance along the incline was smaller -the work done by a force on an object is the energy transferred to the object -work is needed to bring the coaster to the top of hill -work increases the energy of the system -work to lift cart up the ramp is = work to lift it vertically to that height -when you lift vertically, the force = in magnitude to weight of the cart -vertical displacement is the height that it must be lifted W = F x d W = weight x height W = mgh More Roller Coaster Energy -cart is raised with electrical energy supplied by a motor -electrical energy calculated by measuring voltage, current, and time -steam also could raise it -work is done by the spring (by electricity or by heat) -coaster system gains that amount of energy & GPE is increased by that amount -work is also done by friction and air resistance which for example will become heat energy and dissipate into the air Braking the Roller Coaster -brakes use friction to convert KE into thermal energy (heart: friction (brakes) -need back-up too = large spring that could compress, as it compresses, KE is stored as SPE -make a final hill Power power: the work done divided by the time elapsed; the speed at which work is done and energy is transferred P = work done / time elapsed watts: the SI unit for power; 1 W = 1 J/s
PTG 1a. The GPE of the cart at the top of the incline is much greater than the cart at the bottom of the incline. 1b. As the cart went from the top to the bottom, all of the work is done by gravity. 1c. All of the work is don't by the spring as the spring compressed 1d. SPE = 1/2kx^2 1e. The total energy just before it hits the spring is GPE. 1f. You begin to slow down just when you first touch the spring. 2a. W = F x d work is zero because the force and distance are perpendicular, or not in the same direction. 2b. W = F x d W = 60 x .5 W = 30 N 2c. W = F x d W = 75 x 40 W = 3000 N 2d. W = F x d W = 500 x .7 W = 350 N 3. Instead of simply saying to "conserve energy," you could say "conserve energy within a system" because this relates directly to KE, SPE, GPE, and W. This energy is constantly being transferred and conserved except when it is lost to friction, heat energy, sound energy, etc. 4. If clay was added, the mass would increase, so the force would increase. Therefore, the distance it would travel would decrease to keep Work consistent. Then, the GPE and KE would increase 5a. W = F x d W = 10,000 x 20 W = 200,000 N 5b. P = work / change in t P = 200000 / 150 P = 1333 1/3 J/s 6. On the way up the ramp the roller coaster is gaining GPE and the motor is performing work on the roller coaster cart. The work from the motor increases the energy of the roller coaster. At the top, there is not more work by the motor, but there is some work by friction with the air and track. Up the first incline (W --> GPE) down hill (GPE-->KE) up loop at the top (KE & GPE) back curve (KE) up second hill (GPE & KE) horizontal loop (KE) braking (work)
Checking Up 1. When a spring scale is used to do work pulling a cart to the top of an incline, the energy has gone into GPE 2. The roller coaster gets its GPE at the top of the first hill from work done by the spring (electricity or heat) that gains that amount of energy 3. Truckers use a ramp when loading a truck because the force is decreased so it is not as difficult to do. work to lift up the ramp is = work to lift it vertically to that height, when you lift vertically, the force = in magnitude to weight of the cart, vertical displacement is the height that it must be lifted 4. When the brakes stop a roller coaster, the KE is converted into thermal energy 5. The unit for power is watts. 1 W = 1 J/s
What do you think now?
- It takes more energy to pull it up a steep incline because the steeper the incline the more power is needed to move the roller coaster. A gradual incline does not need as much power because it can carry the speed that it already had into it.
Section 9
What do you see?
- There are two people thinking about how to draw a roller coaster on paper. She is doing it by using energy and the boy is thinking about it using force.
What do you think?
- The drop and the turns will be the most thrilling because because that is when you have the most speed.
- If there are turns and drops then it will make it fun. It will not just be a straight ride with no turns or drops.
Physics Talk
Scalar- regular arithmetic to add
Vector- vector addiction techniques that take direction into account
- same direction - add
- opposite direction - subtract
- right angles- Pythagorean Theorem
Checking up 1. Need to use Pythagorean Theorem 2. Energy is a scalar quantity and force is a vector. 3. It tells you that on a ride where friction is insignificant, KE+GPE will always equal the same thing, gravity and mass are constant so the GPE is depended on its height, and if the roller coasters are at the same height, they will be going at the same speed too. 4. The path is not affected 5. Work
Physics Talk 1a. a^2+b^2=c^2 5 ^2 +5^2=c^2 50= c^2 c= rt 50 m/s south west 1b. tan x= 5/5 x= 45 degrees 2. They have the same gravitational potential energy at the top because they start at the same height so at the bottom they will have the same kinetic energy, and therefore the same velocity. 3a. distance- scalar b. displacement- vector c. speed- scalar d. velocity- vector e. acceleration- vector f. force- vector g. kinetic energy- scalar h. potential energy- scalar i. work- vector 4a. scalar b. vector c. scalar d. vector 5. On a ride concerned with energy: The roller coaster approaches the first hill. It uses its kinetic energy and work to get up the hill. At the top it is converted into GPE. As is goes down the hill though it is converted back into kinetic energy. On a ride concerned with force: As the cart goes farther up the hill, there is more weight holding the cart down. The normal force decreases. 6a. picture b.picture c. It is easier to measure the force in roller coaster 2 because it is a straight track. Normal force is always perpendicular to the track which is why it is easier. 7a. picture b. The GPE at all these points are equal because they are at the same height. The cart has the same amount of energy. c. The kinetic energy is equivalent because their GPE is the same. They are going at the same speed. d. You are able to ignore the other points because they are at the same height. The mass and the gravity are always constant so the total GPE is controlled by the height. GPE +KE must always be equal at each point on the roller coaster so because their GPE is the same, the kinetic energy must also.
What do you think NOW?
- When the ride switches from left to right, it will be the most thrilling. This change in direction is a change in velocity. If the speed stays the same during the ride, the ride will be the same because the velocity changes.
Section 10
What do you see?
- There is a very dangerous roller coaster. People are flipping over and falling out of the carts. Some of the tracks are missing which makes it very dangerous.
What do you think?
- Yes because less people are going to go on the ride if they know that there is a chance of them dying.
- Yes because I would not go on any of the rides. They would not be fun and it would just be life threatening.
Physics Talk
- acceleration - safe values --> up to 4 gs
ac = v^2/r
How to fix if values greater than 4 gs
- radius increase
- lower the velocity
- reducing the height of start
- increase the height of the bottom of the loop
Checking up Questions 1.) 4 gs is the maximum safe acceleration.
2.) You can decrease the height of the coaster which will decrease the GPE as well as the kinetic energy. The velocity with get smaller, or you can make the radius of the loop bigger.
3.) At the end of the loop.
4.) At the top of the loop.
Physics To Go
1. I would check the accelerations at each of the points to make sure that it is under 4 gs. This will ensure that the people wont be killed or knocked unconscious. I would also check to make sure that the cart is going fast enough around the loop. If it isn't, the cart won't be able to make it over the loop.
2.a. mgh+1/mv^2
20 m
b. a= v^2/ r
a = 20^2/ 12
a= 400/12
a= 33.33 m/s^2
c. No it is over 4 gs
d. 4g= 39.2 m/s
39.2= v^2/12
470.4= v^2
v= 21.69 m/s
e. 39.2=v^2/ 7
274.4=v^2
v= 16.57 m/s
3.a. a= v^2/r
a= 25^2/ 10
a= 62.5 m/s^2
b. yes safe acceleration
4.a. GPE= MGH
mgh= mv^2
9.8(50)= v^2
490=v^2
v= 31 m/s
b. a= v^2/r
a= 22.14 ^2/ 10
a= 96 m/s^2
c. v= sqrt(a*r)
v= sqrt(49.02*10)
v= 22.14 m/s
d. 58 m/s
e. This roller coaster is safe because the acceleration isn't too high.
5.a. mgh= mv^2
9.8(16)=v^2
v= 8.9 m/s
b. GPE= KE
mgh=1/2mv^2
9.8h= 1/2(12.52)^2
h= 20 m
6.a. a= v^2/r
a= 12^2/18
a= 8 m/s^2
b. F=mv^2/r
F= 900(12)^2 / 18
F= 7,200 N
c. The normal force on the track and the weight will provide the centripetal force.
7.a. a= v^2/r
a= 20^2/15
a= 26.67 m/s^2
b.F= mv^2/r
F= 900(20)^2/15
F= 24,000 N
c. The ride is safe. It is true because the car exerts 24,000 and the ride exerts 25,000. 8.a. It will not change because the mass doesn't affect the centripetal acceleration.
b. It will go the same because the mass doesn't affect it.
c. It might need stronger materials to hold the extra amount of people.
Physics Plus
What do you think NOW?
- People will not go on the roller coaster. The ride might be too dangerous if the speed of it goes faster than 4 gs. A normal human can not take more than 4 gs. Also of the turns and loops are strong enough to hold the carts. The velocity at the top of the loop has to be a certain speed or else they will not be able to make it all the way around the loop.
Table of Contents
Section 1
What do you see?
- A girl is pushing a guy around on a chair. She is making it seem like he is actually on a roller coaster. She is changing directions really fast
What do you think?
- Going down because I believe the stomach drops and you feel really strange and you are going so fast.
Kingda Kaaaaa
- Kingda Ka is a thrilling ride that s located at Six Flags Great Adventure. It is very popular because of its major drop. The ride is a fast ride that only takes like 20 seconds, but the wait is the most thrilling part. You start off by going up really high until you reach the top and come down at a very fast speed. Due to the coaster going so fast, the coster needs to turn on the way down because of the speed.
http://www.sixflags.com/greatadventure/rides/kingdaka.aspx
Nitro
- Nitro also a thrilling ride and is also located at SIx Flags Great Adventure. It is a typical roller coaster made of steel and it moves very fast. Many riders love the thrill of the flips and fast turns that this ride provides. This is also not a slow ride, at it's top speed Nitro can go about 80 mph.
http://www.ultimaterollercoaster.com/coasters/yellowpages/coasters/nitro_sfgadv.shtml
Physics Talk
scalar: a quantity that has magnitude, but no direction (opposite of a vector)
speed: distance traveled divided by time elapsed. scalar
vector: a quantity that has both magnitude and direction
displacement: the difference in positions; it depends only on the endpoints, not on the path. vector
velocity: displacement divided by the time elapsed(vector)
acceleration: the change in velocity divided by the time elapsed. (vector)
Checking up q 1-4
1. The distance is scalar (no direction) and displacement is vector (direction). I
2. Going to school and back, the displacement is 0
3. speed is distance/time- scalar and velocity is displacement/time- vector
4. acceleration = change in velocity / time elapsed
Physics to Go
1.
2. The cause of the thrills is during the accelerations along the curve, drops, and horizontal circles.
3. a) The smaller the radius higher speed. There is more distance to travel and there is less thrills because you are traveling at constant speed
b) V = 40000/ t t = 24 hours
V = 1,666.7 km/hour
4. a = v/t
= 12/4m/s2
= 3 m/s2
5. a) speed
b) velocity
c) velocity
d) displacement velocity
e) displacement
6. v = d/t
v = .1m/2s
.05 m/s
7. v = d/t
.05 m/s = .05m / s
s = 1
8. a = change in V / change in t
a = 25 m/s / 10s
a = 2/5 (m/s)/2
10a) for young children I would make the back curve have a bigger radius so it is slower. For adults make the radius smaller so you go through faster.
10b)
What do you think Now?
Going down the first drop because that is when you have reached the fastest acceleration and you are not used to the speed. The flip is also thrilling but you are going so fast that it is hard to feel heavy.
Section 2
Physics Talk
Gravitational Potential Energy and Kinetic Energy
Energy Transformations in the Roller coaster
GPE: the energy a body possesses as a result of its position in a gravitational field
KE: the energy an object possesses because of its speed
KE depends on speed, GPE depends on height, and both depend on mass
GPE(J)
KE(J)
mechanical energy: the sum of kinetic energy and potential energy
the sum of KE and GPE is the same at any point in the rollercoaster
when GPE increases, KE decreases and vice versa
Calculating KE from GPE
Calculating Speed from Kinetic and GPE
Mechanical energy (bottom) = mechanical energy (top)
KE (bottom) + GPE (bottom) = KE (top) + GPE (top)
1/2mv^2 (bottom) = mgh (top)
What goes up must come down?
What do you see?
- There is a roller coaster and the people in the first car is bored because they are going straight and slow. The second car the people are excited because they are going down a drop and they are going faster.
What do you think?
- The cart at the steeper angle because it is at a bigger angle and it will travel down the slope faster.
Checking up q 1-5
Physics to Go
1. They are the same because they start at the same height
3.
5.
Mass of car = 300 kg and g = 10 N/kg or 10 m/s^2 (approximate value)
73,500 J
0 J
75,000 J
36,750 J
75,000 J
14,700 J
75,000 J
7. GPE = mgh
= (.2)(9.8)(.75)
= 1.47 J
GPE = KE
mgh = 1/2mv^2
(9.8)(.75)
1/2v^23.83 m/s = v
GPE = KE
mgh = 1/2mv^2
(9.8)h = 1/2(3.83)^2
h = .75 m
8. The speed will not change if there are 6 passengers or 26 passengers. The speed is independent of the mass of the car. This is because in the equation GPE (top) = KE (bottom), mass cancels out
9) a. The roller-coaster is traveling at its fastest at point B because its initial height was the highest before the drop. The smallest is GPE and the biggest is KE.
9) b. The roller-coaster is traveling at the same speed at points C and F. This is because their heights are the same. GPE and KE are equal to each other.
9) c. The roller-coaster is traveling faster at D because it was just dropped at point C. Other than traveling up at D.
10) b. The roller coaster cannot reach point H. This is because the height of the original GPE is less than the height of H. With GPE and KE equaling the each other, the height of H would make that it very hard to be higher.
11.
(m)
(J)
(J)
(J)
What do you think now?
- The one with the steeper drop because it feels like you are going down at a different angle. They both have the same speed, but the second one provides more acceleration than the first one. It is more thrilling due to the faster acceleration.
Section 3
What do you see?
One of the kids launches the frog spring toy into the air. A lab partner is standing up with a ruler trying to eye down how high the toy goes into the air. There is also a photo gate towards the bottom of the launch immediately after the frog launches to get its velocity.
What do you think?
To get to its highest point, the roller coaster slowly and gradually climbs up a big hill. No, it does not cost more to lift the people on the roller coaster. No matter how many passengers, the cart is going to make it to the highest point on the roller coaster track.
Physics Talk
Conservation of Energy
- Energy in a system can vary between KE GPE and EPE
- Spring Potential Energy: the energy stored in a spring due to its compression or stretch
ex of EPE: bungee cords, trampolines
EPE = SPE
- a bouncy ball does not get to the same height in each successive bounce because some of the energy is converted to sound/heat energy
- The total energy of an object can be GPE, SPE, or KE, but the sum of the energies is always to same
all energies are measured in joules, and total # of joules must always be the same
pop-up toy: GPE (bottom) KE & some GPE (just after leaving table) equal KE & GPE (halfway up) GPE (top)
a higher mass pop-up toy won't go as high as a lower-mass one even though both had the same SPE.
- The less massive and more massive pop-up toys can have the same GPE if the more massive pop-up toys don't go as high
- Since GPE = mgh, the larger mass has a smaller height and the smaller mass has a larger height
a roller coaster has all its GPE at the highest hill. This becomes KE as the coaster is released.
electric energy pulls the coaster up a hill. The electrical energy comes from a powerplant
after the cars are pulled up to the top of the hill, the total GPE and KE remains the same except for the losses due to thermal and sound energy
- As the breaks stop, KE is converted to thermal energy
- If brakes fail, a large spring may stop the car as the car compresses it
SPE = 1/2kx^2
k=spring constant
x=amount of stretch or compression of the spring
Checking Up Questions
1. As it bounces off of the table, all of the SPE transfers into gravitational potential energy and kinetic energy.
2. Because it has 2J of potential energy, the kinetic energy will be 2J as well.
3. When reaching maximum height, the GPE will be 2J.
4. EPE=1/2kx^2. K is the spring constant and x is the distance compressed/stretched.
Physics To Go
5. The second hill can't be higher than the first. It won't have enough gravitational potential energy to reach the top of the second hill.
6. The roller coaster doesn't travel forever. As it continues to move, it loses its kinetic energy and gravitational potential which turns into heat and sound energy. Then it can't travel forever. 2016730094
7. GPE= electric energy
(300)(9.8)(15)= electric energy
=44,100J
8a. KE= 1/2 mv^2
KE=1/2(400)(15)^2
=45,000J
8b. GPE=KE
=45,000 J
8c. 45,000= (400)(9.8)(h)
11.48 meters=height
9. As a ball is thrown upwards, because the height is increasing, the GPE increases because they are related.
10. The gain is the same for each path because they are all going up to the same height so they will all have the same gravitational potential energy at the end.
11a. They should have similar results because they are the same.
11b. KE=SPE
1/2 mv^2=SPE
SPE= 1/2(0.020)(2.7)^2
SPE=0.0729 J
11c. KE=GPE
1/2mv^2=mgh
1/2(.006)(2.7)^2= (.006)(9.8)h
h= .37m
12a. SPE= 1/2 kx^2
52,920J= 1/2k(4)^2
x= 6,615 Nm/s
12b. GPE= SPE
GPE=mgh
GPE=70,560 J
1/2(6,615)x^2=70,560
x= 4.62m
13. KE= SPE
KE=1/2kx^2
KE=1/2(40)(.3)^2
KE= 1.8 J
What do you think Now?
- The roller coaster needs to have enough speed to get up to the top of the hill. It also needs a strong enough wire to pull it up just in case it does not have enough speed. Also a chain and motor need to be present.
- Yes because the heavier the object the slower it travels up the hill, but the faster it travels down the hill. The more weight the more work. The more work, the more expensive it is to carry the people up.
Section 4
What do you see?
- The first picture they are very bored on the moon. The second picture they are more excited. It is because the moon has no gravity and mars has more gravity than the earth. The more gravity the faster they go.
What do you think?
- Yes. The gravity on earth pulls us towards the center of earth. That is why we can stand.
- Australia looks upside down to us because it is on the other side of the planet. They can stand in australia because on the earth the gravity is pulling towards the center of the earth.
Physics Talk
Newton's Law of Universal Gravitation
Gravitational field: the gravitational influence in the space around a massive object
Earth of the source of its gravitational field because it is the first object that sets up in the space around it
second object interacts with this field--moon (response/test object)
Inverse-Square Relationship
acceleration due to gravity becomes less as an object moves further from the surface of Earth
Inverse-Square Relationship: the relationship between the magnitude of a gravitational force and the distance from the mass. this also describes how electrostatic forces depend on the distance from an electrical charge
force of gravity between 2 objects decreases by the square of the distance between them
Ex: if you triple (3x) the distance, the force is (1/9) the original
Newton's law of universal gravitation: all bodies with mass attract all other bodies with mass; the force is proportional to the product of the two masses and gets stronger as either mass gets larger; the force decreases as the square of the distances between the two bogies increases
: the force of attraction between two bodies due to their masses
Equation of Newton's law of universal gravitation
Fg = (Gm1m2)/r^2 (Fg = force between the bodies, r = the distance between their centers, m1 & m2 = masses of the bodies, G = universal constant equal to 6.67 x 10^-11
The moon orbits Earth and the planets orbit the Sun in elliptical paths
plants don't move in exact ellipses b/c planets tug on on another
Checking Up
1. The direction of the gravitational field in the classroom is to the ground
2. The gravitational field is the strongest near the surface of Earth
3. If you triple the distance between two masses, the force is (1/9) the original
4. Gravity is the force that holds the Moon in its orbit around Earth
5. The shape of the orbit of the plants around the sun is approximately elliptical.
Physics To Go
1. Originally, the gravitational force between two asteroids is 500 N. If the distance between them is doubled, the force would be 125 N (1/4 the original).
2a. Fg would be 1/4 of the original
2b. Fg is 1/9 original
2c. Fg is 1/16 original
3. Gravity is always trusted because it does its job of keeping all humans standing on their feet on the Earth. Gravity is always there because we never see floating objects.
4. Acceleration due to gravity (g) is highest at the bottom of a roller coaster, not the top.
5a. Water on the Earth's side facing the moon is closer to the moon than the center of Earth.
5b. Water moves independently to Earth. There are high tides on those bodies of water facing the moon. The gravitational field of the moon is attracted to the water, making the water rise to the forces. Water does not have as much mass as an entire planet (Earth).
5c. There is not an even distribution of water on the Earth's surface because there are bits of land scattered (islands) throughout the waters. All bodies of water are different distances from the moon and therefore, have different (stronger, weaker) impacted forces of the gravitational field of the moon. This is the inverse-square relationship. The further away from the moon, the more subtle the waves.
6a. If a fish was not impacted by gravity, it would be moved away from the water and into the air, becoming a floating object, and eventually, it will die.
6b. Gravity holds the fish in the water because the mass of a fish is much less than the mass of the Earth. Because masses attract, the large mass of Earth attracts to the small mass of the fish.
7a. 1/4
7b. 1/9
7c. 1/16
7d. 4x
8a. 2x
8b. 3x
8c. 4x
8d. 1/2x
9a. 4x
9b. 9x
9c. 16x
9d. 1/16x
10a. 2x
10b. 9x
10c. 6x
Physics Plus
1. a = v^2 / r
2. v = d/t
(2 x pi x [3.84x10^8) / 2440800
v = 998.505 m/s
3. a = v^2 / r
a = 998.505^2 / 3.84x10^8
a= 0.0025 m/s^2
4. It was pretty close to each other.
What do you think Now?
Gravity has a downward direction, or facing the center core of the Earth. Its the direction of the force on the mass. The earth is acting on the human. People in Australia are still held down to the ground even though gravity to us is supposed to have them upside down. Gravity attracts the mass of the people on earth to the center of the Earth, which means that the people are forced to the surface of the Earth.
Section 5
What do you see?
- Someone buying some type of meat. Weighing the meat by pushing down. In the second picture they are measuring in the air using a spring scale
- Different ways to measure things
What do you think?
- No because a canary will move around and you can't an exact measurement. The elephant is much heavier and might break a spring scale.
Physics Talk
Hooke's Law Describes the Restoring Force a Spring Exerts
Stretching a rubber band or a spring requires a force
There is a linear relationship between the amount of force required for each stretch of the spring.
It is a straight line.
Robert Hooke discovered this property of springs
stretch of spring is directly proportional to the force applied to it
If the spring is not moving, the spring exerts a restoring force equal in magnitude to the force that stretched the string.
Hooke's law: the restoring force exerted by a spring is directly proportional to the distance of stretch or compression of the spring
force exerted by the spring = -spring constant x spring stretch (or compression)
Fs = -kx
negative shows that the pull by the spring is opposite to the direction it is stretched or compressed
k is an indication of how easy or difficult it is to stretch/compress a spring
a stiff spring will have a large value for k; a soft spring will have a small value for k
Hooke's law : F = kx
Straight line: y = slope x
weight = mg
force = ma
weight: the force exerted on a mass as a result of gravity; the weight force on an object due to Earth is downward, in the vertical direction
Stretch and Compress
bathroom scales work by compressing a spring. When you step on the scape, the spring compresses just enough to provide an upward force equal to your weight. The more weight, the more compression of the spring is required. The spring is connected to a scale that has been calibrated to give your weight. As the spring compresses, the arrow points to a different number corresponding to the compression and force of the spring.
Checking Up Questions
1. If the force of the spring is increased 5 times, the stretch of the spring increases 5 times as well (direct relation)
2. Spring constant (k) displays the strength of a spring. The greater value of k, the stiffer the spring. The smaller, the weaker.
3. Mass (in kg) is a part of the weight equation. N=kg*m/s^2. Acceleration must equal 0.
4. The more weight that steps onto the scale, the more compression of the spring inside the scale.
Physics To Go
1a. w=mg
=(100kg)(9.8m/s^2)
=980 N
1b. w=mg
=(10kg)(9.8m/s^2)
=98 N
1c. w=mg
=(60)(9.8)
=588 N
2a. .25/130=1/x
x=578.5 N
2b. 4.45(1000)
x= 4,450 N
2c. 4.45(50)
x=222.5 N
3a.
3b. see above trend lines
3c. The slope of the graph is 14.913 N/m, which is the k (spring constant) value.
3d. The slope represents the k value. This shows the strength/stiffness or weakness of the spring.
3e. I purposefully made the second spring more weak. The slope is 1.8667 N/m. This is the k value, and it is weaker because it has a less steep slope. The spring is weaker than the other one.
4. Fs=-kx
12=k(.03)
k=400N/m
5. As the force of the spring increases, the stretch distance also increases. It is a direct relationship. When clearing the side that K is on, the equation becomes k=Force of spring divided by stretch distance. The greater the value of k, the greater the stiffness of the spring. Therefore, the more force, the less distance it stretches. When weight is added, the stretch distance will increases, but it may not be a dramatic increase. Negative sign indicates that the force is going in the opposite direction of the stretch distance.
6. The greater value of k, the more stiff the spring is. Therefore, 15.0 N/cm is more difficult to stretch.
7. slope= 150N/m *points of slope (.03,4.5)(.01,1.5)
8. A spring scale displays weight in newtons. When attaching masses, the scale stretches, and you can read the scale to determine the weight. It incorporates the mass added and the stretch distance that is created from adding mass. Therefore, it follows the y=-kx formula.
What do you think now?
The same scale can not weigh both a canary and an elephant. The scale works by the compression of a spring. The spring can only hold so much. The scale would be only able to read the maximum number of weight on it, and that will not be the full weight of the elephant. There is not enough distance for the spring to compress for the elephant to go onto the scale.
Section 6
What do you see?
- A big guy is standing on a scale and it is going down because he is so big. Then there is a small person who is getting pulled up because he is litter.
What do you think?
- Your weight does not change but it feels like it is. You are going up and down very quickly, and it throws your weight around.
- Yes because it is pulling you up which makes you seem like you are little and then when you are going down you are pushing down harder than normal.
Physics Talk
Newton's first law
- An object at rest stays at rest, or in motion stays in motion unless acted on by an unbalanced force.
Newton's second law
- unbalanced force creates an acceleration
- The bigger force is in the same direction
- To do this, draw Mation Map (draw FBD)
Checking Up
1. The sum of all the forces acting on an object when it is moving up at constant speed is zero.
2. When accelerating up on a bathroom scale on a roller coaster, the reading on the scale will be greater than your weight in magnitude.
3. You feel as if your weight is more when you accelerate upward because of contact forces and stretching stomach tissues, and forces are holding your stomach in place
4. If the elevator cable were to break, you would only have the force of your weight pulling you down & nothing pushing you up. The force reading on the scale would be zero and you'd feel weightless.
5. Air resistance slows a falling raindrop.
Physics to Go
1.
a. (9.8)(2) = 19.6 m/s
b. (9.8)(5) = 49 m/s
c. (9.8)(10) = 98 m/s
2
a. (1.6)(2) = 3.2 m/s
b. (1.6)(5) = 8 m/s
c. (1.6)(10) = 16 m/s
4.
5. A student who 150 lb and is 148 lb on a scale on an elevator has increased down acceleration, or they decreased their acceleration upward.
6. The person will observe that his weight increases. An increased upward acceleration increases the weight on the scale because the force that the scale is exerting is greater than the force of weight exerted downward.
7
a. When the elevator starts to descend the scale's reading will decrease.
b. Fnet = ma
F=ma
N-mg = ma
N= ma +mg
= (50-1.5) +(50x9.8)
= 415 N
8
a. Scale = 0
w= mg= 50x9.8
= 490 N
b. velocity up/ acceleration up/ f is up
N-mg = ma
N= 50(2) + 490
N= 590 N
c. N-w = ma
N
w= 4909
a. At rest, the force up (scale) and force down (gravitation) are both equal, so the Fnet is zero. When the Fnet = zero, the scale reads your accurate weight.
b. An elevator in free fall has no force from a scale pushing up, so there is only the force of you pushing down. Therefore, the scale reads as 0.
c. The scale reads a greater number than at rest because it is accelerating upward. When acceleration up, that means the bigger force is in the Fscale. When Fscale is bigger than the weight, the number is positive, and the scale will read a higher number.
10. They would find the loops exciting because they feel heavier the whole time in the loop. They'd also like the change between increasing upward/downward acceleration and decreasing upward/downward acceleration. The increase acceleration upward would make them feel heavy and the increase down would change their feeling to light. The decrease upward would then keep them feeling light, but the decrease downward would have them feeling heavier.
Notes
Increasing SPeed: Velocity and Acceleration point in the same direction
-->(v) -->(v) --> (v)
-->(a)
Decreasing Speed: Velocity and acceleration point in opposite directions
-->(v) -->(v) --> (v)
<--(a)
F and acceleration ALWAYS POINT in same DIRECTION
The Bigger force is in same direction as F
What do you think Now?
- No. Your weight does not change because your weight is always the same. Lets say I am standing on a bathroom scale, my weight will not change unless I go up and down because it is a change of direction. If you are going up your acceleration is up and you will be heavier than normal. If you are going down your acceleration will be down and the measurement of your weight on the scale will be smaller.
Section 7
What do you see?
- I see a roller coaster with a bunch of turns and loops. It seems like it is very scary and life threatening because the person in the cart is falling off the tack.
What do you think?
- It is because the carts have so much momentum that they can carry through the entire loop.
Physics Talk
Centripetal Force
- force that points to the center of the circle
- It can either be Normal, Tension, Weight,
Centripital acceleration
- Always points to the center of the circle
- The Speed is constant
- If the centripetal acceleration is equal to 0 then you are moving in a straight line
- Fc= mv^2/r
- The force, net force, and acceleration all point to the center of the circle
safety
- Less than 3 g's is safe for regular people
- Trainer people like astronauts can do like 6 g's
Checking up
1. Centripital force
2. Yes. You must or else you will fall
3. Weight and Normal
4. Normal
5. Mass it is direct relationship and on the radius it is inverse and speed is direct squared
Physics to go
1a. The path is a circle
1b. If the string breaks, the car would travel on a tangent to the circular path.
2a. Friction of the tires replaces the string of the car.
2b. If hitting a patch of ice, you will go tangent to the circular path.
6a. The speed did not change. Velocity has changed.
6b. The velocity changed because it changed direction.
6c. delta V=Vf-Vi
20^2 + 20^2 = c^2
c = 28.2 m/s
tan-1 = 20/20
theta = 45 degrees
7. Ac=v^2/r
=20^2/200
= 2 m/s^2
13a. Bottom of hill #1- heavier
13b. Top of vertical loop- uncertain
13c. Bottom of vertical loop- heavier
13d. Bottom of hill #2- heavier
13e. Lift hill (going up at constant speed)- "normal"
14a. Bottom of hill #1- up
14b. Top of vertical loop- down
14c. Bottom of vertical loop- up
14d. Bottom of hill #2- up
14e. Lift hill (going up at constant speed)- zero
14f. Horizontal loop- to center
14g. Back curve- to center
Physics Plus
1.
a. As mass increases, the net force increases. They share a direct relationship.
b. The velocity and the net force share a direct-square relationship.
2. Fc=mv^2/r. If velocity is doubled, the force needs to be 4 times as strong because of the direct square relationship.
3.The Fnet decreases because the radius increases.
4. The larger radius for the curve, the LESS the force required to keep the car moving along a curve. If the curve is tight, than a GREATER force is required.
5.The more string that was let out, the less force was needed.
6.
a. Ac=v^2/r
=12^2/20
=7.2 m/s^2
b. Fc=mv^2/r
= (300)(12^2)/20
=2160 N
What do you think Now?
- You feel pressed into your seat due to inertia. The net force has to point to the center because if it doesn't then you will fall to the ground. You will not fall because of the forces acting on you that cause you to stick to the cart.
Section 8
Physics Talk
work: the product of displacement and the force in the direction of the displacement; the energy transferred to an object
W = force (parallel to the displacement) x displacement
-W is the same regardless to the angle of the incline
-Force is larger on a steeper incline ; but the distance along the incline was smaller
-the work done by a force on an object is the energy transferred to the object
-work is needed to bring the coaster to the top of hill
-work increases the energy of the system
-work to lift cart up the ramp is = work to lift it vertically to that height
-when you lift vertically, the force = in magnitude to weight of the cart
-vertical displacement is the height that it must be lifted
W = F x d
W = weight x height
W = mgh
More Roller Coaster Energy
-cart is raised with electrical energy supplied by a motor
-electrical energy calculated by measuring voltage, current, and time
-steam also could raise it
-work is done by the spring (by electricity or by heat)
-coaster system gains that amount of energy & GPE is increased by that amount
-work is also done by friction and air resistance which for example will become heat energy and dissipate into the air
Braking the Roller Coaster
-brakes use friction to convert KE into thermal energy (heart: friction (brakes)
-need back-up too = large spring that could compress, as it compresses, KE is stored as SPE
-make a final hill
Power
power: the work done divided by the time elapsed; the speed at which work is done and energy is transferred
P = work done / time elapsed
watts: the SI unit for power; 1 W = 1 J/s
PTG
1a. The GPE of the cart at the top of the incline is much greater than the cart at the bottom of the incline.
1b. As the cart went from the top to the bottom, all of the work is done by gravity.
1c. All of the work is don't by the spring as the spring compressed
1d. SPE = 1/2kx^2
1e. The total energy just before it hits the spring is GPE.
1f. You begin to slow down just when you first touch the spring.
2a. W = F x d
work is zero because the force and distance are perpendicular, or not in the same direction.
2b. W = F x d
W = 60 x .5
W = 30 N
2c. W = F x d
W = 75 x 40
W = 3000 N
2d. W = F x d
W = 500 x .7
W = 350 N
3. Instead of simply saying to "conserve energy," you could say "conserve energy within a system" because this relates directly to KE, SPE, GPE, and W. This energy is constantly being transferred and conserved except when it is lost to friction, heat energy, sound energy, etc.
4. If clay was added, the mass would increase, so the force would increase. Therefore, the distance it would travel would decrease to keep Work consistent. Then, the GPE and KE would increase
5a. W = F x d
W = 10,000 x 20
W = 200,000 N
5b. P = work / change in t
P = 200000 / 150
P = 1333 1/3 J/s
6. On the way up the ramp the roller coaster is gaining GPE and the motor is performing work on the roller coaster cart. The work from the motor increases the energy of the roller coaster. At the top, there is not more work by the motor, but there is some work by friction with the air and track. Up the first incline (W --> GPE) down hill (GPE-->KE) up loop at the top (KE & GPE) back curve (KE) up second hill (GPE & KE) horizontal loop (KE) braking (work)
Checking Up
1. When a spring scale is used to do work pulling a cart to the top of an incline, the energy has gone into GPE
2. The roller coaster gets its GPE at the top of the first hill from work done by the spring (electricity or heat) that gains that amount of energy
3. Truckers use a ramp when loading a truck because the force is decreased so it is not as difficult to do. work to lift up the ramp is = work to lift it vertically to that height, when you lift vertically, the force = in magnitude to weight of the cart, vertical displacement is the height that it must be lifted
4. When the brakes stop a roller coaster, the KE is converted into thermal energy
5. The unit for power is watts. 1 W = 1 J/s
What do you think now?
- It takes more energy to pull it up a steep incline because the steeper the incline the more power is needed to move the roller coaster. A gradual incline does not need as much power because it can carry the speed that it already had into it.
Section 9
What do you see?
- There are two people thinking about how to draw a roller coaster on paper. She is doing it by using energy and the boy is thinking about it using force.
What do you think?
- The drop and the turns will be the most thrilling because because that is when you have the most speed.
- If there are turns and drops then it will make it fun. It will not just be a straight ride with no turns or drops.
Physics Talk
Scalar- regular arithmetic to add
Vector- vector addiction techniques that take direction into account
- same direction - add
- opposite direction - subtract
- right angles- Pythagorean Theorem
Checking up
1. Need to use Pythagorean Theorem
2. Energy is a scalar quantity and force is a vector.
3. It tells you that on a ride where friction is insignificant, KE+GPE will always equal the same thing, gravity and mass are constant so the GPE is depended on its height, and if the roller coasters are at the same height, they will be going at the same speed too.
4. The path is not affected
5. Work
Physics Talk
1a.
a^2+b^2=c^2
5 ^2 +5^2=c^2
50= c^2
c= rt 50 m/s south west
1b. tan x= 5/5
x= 45 degrees
2. They have the same gravitational potential energy at the top because they start at the same height so at the bottom they will have the same kinetic energy, and therefore the same velocity.
3a. distance- scalar
b. displacement- vector
c. speed- scalar
d. velocity- vector
e. acceleration- vector
f. force- vector
g. kinetic energy- scalar
h. potential energy- scalar
i. work- vector
4a. scalar
b. vector
c. scalar
d. vector
5. On a ride concerned with energy: The roller coaster approaches the first hill. It uses its kinetic energy and work to get up the hill. At the top it is converted into GPE. As is goes down the hill though it is converted back into kinetic energy.
On a ride concerned with force: As the cart goes farther up the hill, there is more weight holding the cart down. The normal force decreases.
6a. picture
b.picture
c. It is easier to measure the force in roller coaster 2 because it is a straight track. Normal force is always perpendicular to the track which is why it is easier.
7a. picture
b. The GPE at all these points are equal because they are at the same height. The cart has the same amount of energy.
c. The kinetic energy is equivalent because their GPE is the same. They are going at the same speed.
d. You are able to ignore the other points because they are at the same height. The mass and the gravity are always constant so the total GPE is controlled by the height. GPE +KE must always be equal at each point on the roller coaster so because their GPE is the same, the kinetic energy must also.
What do you think NOW?
- When the ride switches from left to right, it will be the most thrilling. This change in direction is a change in velocity. If the speed stays the same during the ride, the ride will be the same because the velocity changes.
Section 10
What do you see?
- There is a very dangerous roller coaster. People are flipping over and falling out of the carts. Some of the tracks are missing which makes it very dangerous.
What do you think?
- Yes because less people are going to go on the ride if they know that there is a chance of them dying.
- Yes because I would not go on any of the rides. They would not be fun and it would just be life threatening.
Physics Talk
- acceleration - safe values --> up to 4 gs
ac = v^2/r
How to fix if values greater than 4 gs
- radius increase
- lower the velocity
- reducing the height of start
- increase the height of the bottom of the loop
Checking up Questions
1.) 4 gs is the maximum safe acceleration.
2.) You can decrease the height of the coaster which will decrease the GPE as well as the kinetic energy. The velocity with get smaller, or you can make the radius of the loop bigger.
3.) At the end of the loop.
4.) At the top of the loop.
Physics To Go
1. I would check the accelerations at each of the points to make sure that it is under 4 gs. This will ensure that the people wont be killed or knocked unconscious. I would also check to make sure that the cart is going fast enough around the loop. If it isn't, the cart won't be able to make it over the loop.
2.a. mgh+1/mv^2
20 m
b. a= v^2/ r
a = 20^2/ 12
a= 400/12
a= 33.33 m/s^2
c. No it is over 4 gs
d. 4g= 39.2 m/s
39.2= v^2/12
470.4= v^2
v= 21.69 m/s
e. 39.2=v^2/ 7
274.4=v^2
v= 16.57 m/s
3.a. a= v^2/r
a= 25^2/ 10
a= 62.5 m/s^2
b. yes safe acceleration
4.a. GPE= MGH
mgh= mv^2
9.8(50)= v^2
490=v^2
v= 31 m/s
b. a= v^2/r
a= 22.14 ^2/ 10
a= 96 m/s^2
c. v= sqrt(a*r)
v= sqrt(49.02*10)
v= 22.14 m/s
d. 58 m/s
e. This roller coaster is safe because the acceleration isn't too high.
5.a. mgh= mv^2
9.8(16)=v^2
v= 8.9 m/s
b. GPE= KE
mgh=1/2mv^2
9.8h= 1/2(12.52)^2
h= 20 m
6.a. a= v^2/r
a= 12^2/18
a= 8 m/s^2
b. F=mv^2/r
F= 900(12)^2 / 18
F= 7,200 N
c. The normal force on the track and the weight will provide the centripetal force.
7.a. a= v^2/r
a= 20^2/15
a= 26.67 m/s^2
b.F= mv^2/r
F= 900(20)^2/15
F= 24,000 N
c. The ride is safe. It is true because the car exerts 24,000 and the ride exerts 25,000.
8.a. It will not change because the mass doesn't affect the centripetal acceleration.
b. It will go the same because the mass doesn't affect it.
c. It might need stronger materials to hold the extra amount of people.
Physics Plus
What do you think NOW?
- People will not go on the roller coaster. The ride might be too dangerous if the speed of it goes faster than 4 gs. A normal human can not take more than 4 gs. Also of the turns and loops are strong enough to hold the carts. The velocity at the top of the loop has to be a certain speed or else they will not be able to make it all the way around the loop.